Purpose The aim of this work is to prove a strong law of large numbers for a sequence of independent compactly uniformly integrable random sets with values in the family of convex closed subsets of a separable Banach space E, again without requiring any geometric conditions on E. Design/methodology/approach Our approach in this work is based on several theories; probability and its application to strong law of large numbers, properties of random sets, convex analysis and functional analysis. Findings This article establishes two strong laws of large numbers for independent, compactly uniformly integrable random sets. Originality/value This paper presents original results concerning the Strong Law of Large Numbers (SLLN) for random sets, specifically focusing on compactly uniformly integrable random sets in separable Banach spaces.
Allali et al. (Thu,) studied this question.